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GeSi Raman spectra vs. local clustering/anticlustering: Percolation scheme and

*ab initio* calculations

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10.1063/1.4813513

### Abstract

We formalize within the percolation scheme that operates along the linear chain approximation, i.e., at one dimension (1D), an intrinsic ability behind Raman scattering to achieve a quantitative insight into local clustering/anticlustering in an alloy, using GeSi as a case study. For doing so, we derive general expressions of the individual fractions of the six GeSi percolation-type oscillators [1 (Ge-Ge), 3 (Ge-Si), 2 (Si-Si)], which monitor directly the Raman intensities, via a relevant order parameter . This is introduced by adapting to the 1D oscillators of the GeSi-diamond version of the 1D-percolation scheme, i.e., along a fully consistent 1D treatment, the approach originally used by Verleur and Barker for the three-dimensional (3D) oscillators of their 1D-cluster scheme applying to zincblende alloys [H. W. Verleur and A. S. Barker, Phys. Rev. 149, 715 (1966)], a somehow problematic one in fact, due to its 3D–1D ambivalence. Predictive -dependent intensity-interplays between the Ge 0.5Si0.5 Raman lines are confronted with existing experimental data and with ab initio Raman spectra obtained by using (32-atom) disordered supercells matching the required values, with special attention to the Ge-Si triplet and to the Si-Si doublet, respectively.

© 2013 AIP Publishing LLC

Received 19 April 2013
Accepted 24 June 2013
Published online 17 July 2013

Acknowledgments: We are grateful to A. V. Postnikov for a critical reading of the manuscript and many useful discussions, and also to M. I. Alonso for stimulating our interest on clustering/anticlustering issues in GeSi. This work was supported by the European funding of Region Lorraine under Project FEDER-Percalloy No. presage 34619. V.J.B.T. would like to thank for funding by the Fundação para a Ciência e a Tecnologia, Portugal (FCT) under the Grant PEst-C/CTM/LA0025/2011.

Article outline:

I. INTRODUCTION

II. GeSi RAMAN SPECTRA IN THEIR DEPENDENCE ON CLUSTERING/ANTICLUSTERING—MAIN FEATURES IN THE LITERATURE

III. GENERALIZED -DEPENDENT VERSION OF THE GeSi PERCOLATION SCHEME

A. Expression of the individual fractions of percolation-type GeSi 1D-oscillators in their dependence on

B. Percolation/MREI-like -dependent Ge_{0.5}Si_{0.5} Raman lineshapes

C. Percolation vs. experimental insights—Main (Ge-Ge, Ge-Si, Si-Si) features and (Ge-Si) triplet

IV. PERCOLATION VS. *AB INITIO* INSIGHTS—(Si-Si) DOUBLET

A. Basic assignment via limit *ab initio* frequencies

B. Raman-intensity aspect

C. Raman-frequency aspect

V. CONCLUSION

/content/aip/journal/jap/114/3/10.1063/1.4813513

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/content/aip/journal/jap/114/3/10.1063/1.4813513

2013-07-17

2014-04-17

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